It from Qubit: How to Draw Quantum Contextuality†

† This paper is a slightly updated version of a fourth-prize winning essay at the contest "It from Bit and Bit from It" of the Foundational Questions Institute in June 2013. The technical material of this note was substantially expanded from Planat et al. Quantum contextual finite geometries from dessins d'enfants. 2013, arXiv:1310.4267v2 [quant-ph].

Abstract

Wheeler’s observer-participancy and the related it from bit credo refer to quantum non-locality and contextuality. The mystery of these concepts slightly starts unveiling if one encodes the (in)compatibilities between qubit observables in the relevant finite geometries. The main objective of this treatise is to outline another conceptual step forward by employing Grothendieck’s dessins d’enfants to reveal the topological and (non)algebraic machinery underlying the measurement acts and their information content.

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